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The '''Hamiltonian''' is a quantity of great importance in both [[classical mechanics|classical]] and [[quantum mechanics]].  

The '''Hamiltonian''' is a quantity of great importance in both [[classical mechanics|classical]] and [[quantum mechanics]]. Whereas the [[Lagrangian Dynamics|Lagrangian]] treats each generalised coordinate and its rate of change as independent, the Hamiltonian treats the generalised coordinate and its canonically conjugate momentum as independent. Lagrangian mechanics produces <math>N</math> second order differential equations, one for each generalised coordinate. Hamiltonian mechanics leads to <math>2N</math> first order differential equations, which makes it often easier for solving problems computationally.

== Classical mechanics ==

== Classical mechanics ==